1. Field of the Invention
The present invention relates to a method of multi-scale reconstruction of the image of the structure of a body. The invention is more particularly applicable to the medical field in the reconstruction of the internal structures of patients under examination. Potential applications can nevertheless be found in other fields, especially in nondestructive industrial testing in which examinations of the same type as medical examinations are performed. The aim of the method in accordance with the invention is to increase the speed of three-dimensional reconstruction when the reconstruction algorithms are iterative algorithms.
2. Description of the Prior Art
Acquisition protocols employed in medicine for determining the internal structures of a body are already known. These protocols are essentially of the following types: tomodensitometry, NMR, ultrasonics, scintigraphy. In these protocols, parts of a patient's body are subjected to an examination. This examination involves several series of measurements in order to make it possible, for example, to reconstruct and display the three-dimensional image of the internal structure of the body. Each series is distinguished from another by the modification of a parameter of the series of measurements or of the experimentation. In tomodensitometry, for example, the parameter concerns the orientation of the tomodensitometer. IN NMR, the parameter may concern the value of a section-selection gradient pulse. In all cases, several series of results of measurements are thus acquired. Each series is representative of the body and of the corresponding configuration of the experimentation characteristic.
In order to reconstruct from series of measurements the three-dimensional image of internal structures under examination, there essentially exist two types of reconstruction algorithm in x-ray imaging. A first type is concerned with a calculation involving back-projection and filtering or else reconstruction by multidimensional Fourier transform. A second type with which the invention is concerned relates to the iterative methods of reconstruction also known as algebraic methods. This second type finds a particular application in tomodensitometry because the utilization of algorithms of the first type leads to unstable solutions in the event of volume reconstruction from a small number of views. The principle of an algebraic algorithm of this type, an improvement of which was described in a French patent Application filed by the present Applicant on Jan. 20, 1989 under No. 89 00676, is described below.
The initial step consists in estimating a priori the shape of the structure of the body under examination. This means that, in the case of all the volume elements or voxels of said body under examination, it is considered that the value of the physical property tested by the experimentation has a known value such as 0, for example. This theoretical object (which in no way resembles the object the property of which it is sought to be determined is then subjected mathematically to a series of experiments which are similar to those to which the body to be examined has really been subjected. The simulation thus performed also leads to several series of "measurements" designated as reprojections, for example, of the (false) theoretical object in accordance with the same configurations of the experimentation characteristic. A comparison is then made between the series of measurements and the series of reprojections and, in the respective series, between each pair of values so as to deduce from the deviation which is found a corresponding modification of the value of the physical quantity in the voxel concerned. The theoretical estimation of said object is modified accordingly.
The next step consists in reiterating this experimentation simulation operation and in also reiterating the comparison of the reprojection series newly obtained with the same series of measurements really measured in the body. A second deviation is deduced therefrom and used to remodify the knowledge of the body structure which had previously been obtained. Thus in a sequence of operations, the estimation of the three-dimensional image of the body structure is refined.
It should be indicated that the real measurements are acquired with a given resolution and that the reconstruction of the image of the body will also be performed with a given resolution. In order to ensure that the resolution of the measurements and the resolution of reconstruction may be clearly differentiated, this latter will be referred-to hereinafter as a fineness of reconstruction. It is known that the resolution of the measurements at the moment of acquisitions leads in correspondence to a significant fineness of reconstruction of the body under examination. A fineness is significant if it really corresponds to a knowledge which is as accurate as possible, taking into account the resolution of the measurements performed. In fact, if the image of a structure is known in accordance with a given fineness and is expressed with a greater degree of fineness by means of any suitable methods of enlargement, its significant fineness is not increased. In the final analysis, one only makes use of the information acquired. This can be compared with the grain of a positive photographic print which can never have a resolution higher than the grain of the negative employed for taking the photograph, irrespective of the enlargement techniques employed.
As can readily be understood, practitioners endeavor to determine the images of the structures being studied with the greatest possible fineness. When conducting experiments, this automatically involves the need to carry out series of measurements with the highest possible resolution. The disadvantage of high resolution and a high degree of reconstructed fineness lies in the duration of the reconstruction calculations which have to be contemplated. This is particularly true in the case of iterative methods in which the calculations are undertaken several times, usually at least twice.
In the invention, this problem of duration of calculations is solved while noting that, in the case of the first iterations, it is not necessary to perform the calculations either with very high resolution or with a very high degree of fineness. In fact, the deviations evaluated during the first iterations are so substantial that they do not need to be evaluated very accurately. It is apparent, for example, that it is not necessary to determine up to the third decimal point the value of a physical quantity measured in a voxel when it is known that the result may already be erroneous at the first decimal point. However, the invention is not concerned with the floating character of this precision which, on close scrutiny, would not result in a significant reduction of calculation times. In conventional practice, the iteration operations in fact involve series of multiplications and additions, the elementary time duration of which is unrelated to the bit number to be processed. There is in fact a continuous parallel processing operation. This time-duration is rather related to the fact that these operations have to follow each other. Thus a following operation uses as arguments the results of a preceding operation.
It has been observed in accordance with the invention that, in the case of the first iterations, it was not necessary to express the reconstructed volume with the final degree of fineness but that, on the contrary, it was possible to use a lower degree of fineness than the final fineness. At the same time, a lower resolution of measurements than the final resolution is employed. The term "final" is attributed to the highest fineness in which the practitioner then desires to see the images. For the resolution of measurements, the final resolution is that which is employed last in the calculations (it is also the resolution really acquired during experiments). In other words, instead of endeavoring to express values of physical quantities in each voxel of the structure, it is endeavored to represent this structure by macro-voxels during preliminary iterations. Before carrying out the final iterations, these macro-voxels are converted by means of an enlargement operation (zoom) to voxels distributed with the final degree of fineness. As will be readily apparent, measurements with lower resolution are employed for calculation of physical quantities at the level of the macro-voxels.